Verify Green's Theorem for Jo where C' is a triangle with vertices (0,0), (1, 3), and (1,5) traced out counter-clockwise by (a) computing the line integral directly and (b) using Green's Theorem to compute the integral. (6y-3y² + x) dx + yx³ dy

Q: Green’s Theorem for line integrals Use either form of Green’sTheorem to evaluate the following line…

A: By Green's Theorem, we have where R is the region enclosed by curve C.

Q: 3) Consider (a) Calculate the line integrals F(x, y, z) = −7+ (²²₂2) 5+ yzk 2 [ F(7) - dr Ja along…

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Q: Use Green's Theorem to evaluate the following line integral. Assume the curve is oriented…

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Q: Consider the line integral xy dx + xy° dy with C the triangle with vertices (0, 0). (1,0), and (1,…

A: Given, the line integral Where C is the triangle with vertices.

Q: cV4-x² Rewrite the integral (3) x – y dz dy dx in spherical coordi- -x² -y? nates. Do NỘT evaluate…

A: We are given a triple integral ∫-22∫04-x2∫-4-x2-y20 x-y dzdydx whose coordinates are x, y, z. We…

Q: I don't understand why R0=C2+C3lnr

A: Please check step 2 for the solution.

Q: Q.2: Let C be the line joining A(-1,0), B(0,1), D(1,1), and E(2,0). Evaluate: Scy dz tor and radius…

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Q: Consider the following line integral. fxy dx + x²y³ xy dx + x²y³ dy, C is counterclockwise around…

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Q: Evaluate the line integral (2x - y + 5)dx + (5y + 3x - 6)dy, for which the path C C traverses around…

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Q: Jo F dr, where F = (3-2y, x-1, -2z) and C is the boundary of a triangle with vertices (0, 0, -3),…

A: Given F=3-2y, x-1, -2z C is the boundary of a triangle with vertices (0, 0, -3), (0, 4, 5), (2, 0,…